DOCS. 66, 67 MARCH 1915 79 applies, i.e., -g has a tensor character.- It is thus quite superfluous to introduce some limit to replace the Auv’s; the derivation is independent of it. Any consideration in which the ôguv’s are sub- jected to more constraints than is necessary for the nature of the problem must be rejected as an unnecessary complication. With cordial greetings, yours, A. Einstein. 67. From Tullio Levi-Civita [Padova,] 28 March 1915 Dearest Colleague, Yesterday I received your postcard of the 20th,[1] and it is with much pleasure that I reply to it immediately, as you requested. In your view, my observation [that there are adapted (angepasste) coordinate systems for which tensor Euv does not vanish, while it is zero when the guv's are constant][2] is not conclusive, because a generic gravitational field cannot be obtained with the help of a coordinate transformation starting from a Euclidean ds2 (guv constant). This is indeed the case. Therefore it is necessary to give a concrete example in which not all Euv's vanish as a result of some admissible transformation from a Euclidean ds2 (contrary to what covariance would require). This is how we go about it. We start from a coordinate system in which ds2 has the canonical Euclidean form ds2 = dx21 + dx22 + dx23 + dx24 (guv = 6uv), and we proceed to perform an infinitesimal transformation, putting x'u = xu + yu, (1) where the yu's designate (a priori any) infinitesimal functions of x. Putting ^uv + huv (2) for the guv's relative to the new variables x', we have hßn - dVn dyv\ dxu dXf,,) (3)